Abstract
There is an approach due to Bazhanov and Reshetikhin for solving integrable RSOS models which consists of solving the functional relations which result from the truncation of the fusion hierarchy. We demonstrate that this is also an effective means of solving integrable vertex models. Indeed, we use this method to recover the known Bethe Ansatz solutions of both the closed and open XXZ quantum spin chains with U(1) symmetry. Moreover, since this method does not rely on the existence of a pseudovacuum state, we also use this method to solve a special case of the open XXZ chain with nondiagonal boundary terms.
Similar content being viewed by others
Reference
H. Bethe, Z. Phys. 71:205(1931); translated in The Many-Body Problem, D. C. Mattis, ed. (World Scientific, 1993).
R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, 1982).
F. C. Alcaraz, M. N. Barber, M. T. Batchelor, R. J. Baxter, and G. R. W. Quispel, J. Phys. A 20:6397(1987).
L. D. Faddeev and L. A. Takhtajan, Russ. Math. Surv. 34:11(1979).
P. P. Kulish and E. K. Sklyanin, Phys. Lett. A 70:461(1979).
E. K. Sklyanin, J. Phys. A 21:2375(1988).
N. Yu. Reshetikhin, Sov. Phys. JETP 57:691(1983).
E. K. Sklyanin, Quantum Inverse Scattering Method. Selected Topics, hep-th/9211111.
G. E. Andrews, R. J. Baxter, and P. J. Forrester, J. Stat. Phys. 35:193(1984).
V. V. Bazhanov and N. Yu. Reshetikhin, Int. J. Mod. Phys. A 4:115(1989).
H. J. de Vega and A. González-Ruiz, J. Phys. A 26:L519(1993).
S. Ghoshal and A. B. Zamolodchikov, Int. J. Mod. Phys. A 9:3841(1994).
R. I. Nepomechie, J. Phys. A 34:9993(2001).
R. I. Nepomechie, Nucl. Phys. B 622:615(2002)
R. I. NepomechieAddendum, Nucl. Phys. B 631:519(2002).
A. A. Belavin and Yu. Stroganov, Phys. Lett. B 466:281(1999).
A. A. Belavin, S. Yu. Gubanov, and B. L. Feigin, Truncation of Functional Relations in the XXZ Model, hep-th/0008011.
P. P. Kulish and E. K. Sklyanin, Lecture Notes in Physics, Vol. 151 (Springer, 1982), p. 61.
V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method, Correlation Functions and Algebraic Bethe Ansatz (Cambridge University Press, 1993).
P. P. Kulish, N. Yu. Reshetikhin, and E. K. Sklyanin, Lett. Math. Phys. 5:393(1981).
A. G. Izergin and V. E. Korepin, Sov. Phys. Doklady 26:653(1981)
A. G. Izergin and V. E. KorepinNucl. Phys. B 205:401(1982).
A. N. Kirillov and N. Yu. Reshetikhin, J. Sov. Math. 35:2627(1986)
A. N. Kirillov and N. Yu. ReshetikhinJ. Phys. A 20:1565(1987).
P. P. Kulish and N. Yu. Reshetikhin, J. Sov. Math. 23:2435(1983).
R. J. Baxter and P. A. Pearce, J. Phys. A 15:897(1982).
R. J. Baxter, Adv. Stud. Pure Math. 19:95(1989).
A. Kuniba, T. Nakanishi, and J. Suzuki, Int. J. Mod. Phys. A 9:5215(1994).
I. V. Cherednik, Theor. Math. Phys. 61:977(1984).
L. Mezincescu and R. I. Nepomechie, J. Phys. A 25:2533(1992).
Y.-K. Zhou, Nucl. Phys. B 458:504(1996).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nepomechie, R.I. Functional Relations and Bethe Ansatz for the XXZ Chain. Journal of Statistical Physics 111, 1363–1376 (2003). https://doi.org/10.1023/A:1023016602955
Issue Date:
DOI: https://doi.org/10.1023/A:1023016602955